Named after Apollonius of Perga, an Apollonian gasket starts with three mutually tangent circles packed inside a bounding circle. The tiny curved-triangle gap left between any three tangent circles can always be filled with exactly one more circle tangent to all three — and repeating that step forever produces a fractal of infinitely many, infinitely shrinking circles that still leaves zero area uncovered.
Apollonian gaskets are not just decorative — their curvatures, when the starting circles have integer curvature, are always integers too (a fact tied to number theory and Ford circles), and the fractal's boundary has a measured dimension of about 1.3057, strictly between a line and a filled disc.
Three mutually tangent circles inside a boundary circle spawn an infinite cascade of ever-smaller tangent circles filling every remaining gap — a real fractal built live from Descartes' Circle Theorem, rendered as a receding 3D disc tunnel.
Every curved-triangle gap between three tangent circles has an exact, computable circle that fills it, found from the circles' curvatures alone via Descartes' Circle Theorem — and repeating the rule forever never runs out of gaps.
Adjust recursion depth and the starting radius ratio to reshape the gasket, use relief depth to turn the flat fractal into a 3D tunnel, and switch colour mode to see generation depth or circle size. Drag to orbit, scroll to zoom.
When the starting circles have integer curvatures, every circle in the entire infinite gasket also has an integer curvature — a surprising link between this ancient geometry problem and modern number theory.